Question

A two digit number is obtained either by multiplying the sum of the digits by 8 and then subtracting 5or by multiplying the difference of digits by 16 and adding 3.Find the number.

Answer 1

Answer:

Let the two digit no. be 10x+y.

Given: Case I

10x+y=8(x+y)-5

10x+y=8x+8y -5

10x-8x+y-8y=-5

2x-7y=-5 (i)

Case II

:10x+y=16 (x-y)+3

:10x+y=16x-16y+3

:y+16y=16x-10x+3

6x-17y=-3 (ii)

Solving eq. (i) and (ii)

Multiplying eq. (i) by 3

6x-21y=-15 (i)

6x-17y=-3 (ii)

So,

On subtracting

-4y=-12

4y=12

y=12/4

y=3

And

2x-7y=-5

2x-7×3=-5

2x-21=-5

2x=-5+21

2x=16

x=16/2

x=8

Hence, no. is 10x+y

=10×8+3

=80+3

=83.

Answer 2

Answer:

Step-by-step explanation:

let first digit be 1

Let second digit be 2

Add 1+2 ie 3

Now multiply 3 by 8 and subtract 5 from that

3x8=24

24-5=19

Subtract 2-1 i.e 1

Multiply 1 by 16

You will get 16 add 3 to that

16+3 =19